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A New Generalization of the Truncated Gumbel Distribution with Quantile Regression and Applications

Author

Listed:
  • Héctor J. Gómez

    (Departamento de Ciencias Matemáticas y Físicas, Facultad de Ingeniería, Universidad Católica de Temuco, Temuco 4780000, Chile)

  • Karol I. Santoro

    (Departamento de Estadística y Ciencia de Datos, Facultad de Ciencias Básicas, Universidad de Antofagasta, Antofagasta 1240000, Chile)

  • Diego Ayma

    (Departamento de Matemáticas, Facultad de Ciencias, Universidad Católica del Norte, Antofagasta 1240000, Chile)

  • Isaac E. Cortés

    (Facultad de Ciencias, Universidad Arturo Prat, Avenida Arturo Prat 2120, Iquique 1110939, Chile)

  • Diego I. Gallardo

    (Departamento de Estadística, Facultad de Ciencias, Universidad del Bío-Bío, Concepción 4081112, Chile)

  • Tiago M. Magalhães

    (Department of Statistics, Institute of Exact Sciences, Federal University of Juiz de Fora, Juiz de Fora 36036-900, MG, Brazil)

Abstract

In this article, we introduce a new model with positive support. This model is an extension of the truncated Gumbel distribution, where a shape parameter is incorporated that provides greater flexibility to the new model. The model is parameterized in terms of the p-th quantile of the distribution to perform quantile regression in this model. An extensive simulation study demonstrates the good performance of the maximum likelihood estimators in finite samples. Finally, two applications to real datasets related to the level of beta-carotene and body mass index are presented.

Suggested Citation

  • Héctor J. Gómez & Karol I. Santoro & Diego Ayma & Isaac E. Cortés & Diego I. Gallardo & Tiago M. Magalhães, 2024. "A New Generalization of the Truncated Gumbel Distribution with Quantile Regression and Applications," Mathematics, MDPI, vol. 12(11), pages 1-20, June.
    • Handle: RePEc:gam:jmathe:v:12:y:2024:i:11:p:1762-:d:1409479
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    References listed on IDEAS

    as
    1. Saravanan Bhaskaran & Amrit Shankar Verma & Andrew J. Goupee & Subhamoy Bhattacharya & Amir R. Nejad & Wei Shi, 2023. "Comparison of Extreme Wind and Waves Using Different Statistical Methods in 40 Offshore Wind Energy Lease Areas Worldwide," Energies, MDPI, vol. 16(19), pages 1-26, October.
    2. Kang, Dongbum & Ko, Kyungnam & Huh, Jongchul, 2015. "Determination of extreme wind values using the Gumbel distribution," Energy, Elsevier, vol. 86(C), pages 51-58.
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